Residents of Partoburg often violate traffic rules, get into accidents involving scooters, and steal other people's scooters. In order to control scooter-related incidents, the sheriff of Partoburg has introduced a scooter registration system.
On the first day of each month the sheriff chooses a natural number $$$n$$$ and prints all possible scooter numbers in the format $$$[a_{1}+a_{2}+ \ldots +a_{k}]$$$, where $$$a_1+a_2+\ldots+a_k = n$$$, and natural numbers $$$a_{i}$$$ are ordered non-decreasingly: $$$a_1 \le a_2 \le \ldots \le a_{k}$$$. Each number is unique: there cannot be two scooters with the same number. The numbers are assigned to scooter owners. If an owner does not have a number in a given month, he cannot use the scooter during that month.
The sheriff himself also moves around on a scooter. To easily identify his scooter, it has a special number format. The sheriff's scooter number is a single number calculated as follows. For all scooter numbers in the current month $$$[a_{1}+a_{2}+ \ldots +a_{k}]$$$, the value $$$\mathrm{mex}{a_{1},a_{2}, \ldots, a_{k}}$$$ is calculated — the minimum natural number absent in the number. These values are summed. The number of the sheriffs scooter is a remainder of the division of the resulting sum by $$$10^9+7$$$.
The sheriff wants to automate the scooter number assignment system and started with his own scooter. This month he chose the number $$$n$$$. Help determine what number his scooter will receive.
In the first line of input is a single natural number $$$n$$$ — the number chosen by the sheriff for this month ($$$1 \le n \le 1000$$$).
Output a single integer — the sheriff's scooter number: an integer from $$$0$$$ to $$$10^9+6$$$, the remainder of the division by $$$10^9+7$$$ of the sum of all the scooter numbers' $$$\mathrm{mex}$$$ values for this month.
1
2
3
6
In the first example $$$n = 1$$$. The only possible number is $$$[1]$$$. In this case the sheriff's scooter number will be $$$\mathrm{mex}{1} = 2$$$.
In the second example $$$n = 3$$$. All possible numbers are $$$[1+1+1]$$$, $$$[1+2]$$$, $$$[3]$$$. In this case the sheriff's scooter number will be $$$\mathrm{mex}{1, 1, 1} + \mathrm{mex}{1, 2} + \mathrm{mex}{3} = 2 + 3 + 1 = 6$$$.
